I was asked this question by a friend's daughter a few days back, and I was interested to see what people here think.
I realize of course that this is quite subjective, but still, I get the impression that certain fields, like algebraic geometry, require much more "initial outlay' in terms of absorbing difficult concepts than others, before one can contribute.
So, what are your experiences ? Is there any consensus among mathematicians about which areas are especially "hard" or "difficult to get into" ?

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9

This should be community wiki. It also runs the risk of being purely subjective. Are we just taking an opinion poll, or is there more to it than that?
–
Pete L. ClarkMay 12 '10 at 13:46

5

Sorry, I'm voting to close. If there is a consensus about hardest area, I haven't heard it.
–
S. Carnahan♦May 12 '10 at 14:02

3

I'm also voting to close. The "hardest area" will depend strongly on the student. I don't think there is any kind of consensus.
–
Andy PutmanMay 12 '10 at 14:10

Perhaps could we put this question in another form than ordering ? === I hope that Mathoverflow could prove in the long run to be a resource to store useful mathematical folklore before it finds its way in books and treatises. In the meantime we could say: in which area of mathematics do you think good textbooks are sorely needed in english ?
–
ogerardMay 12 '10 at 14:51